A pendulum consists of a bob of mass m attached to a string of length L. It is released from rest at an angle θ from the vertical. What is the speed of the bob at its lowest point?

Core Concept

Using conservation of energy, the potential energy at the initial position equals the kinetic energy at the lowest point. The height difference is h = L(1-cosθ). So mgh = (1/2)mv², which gives v = √(2gh) = √(2gL(1-cosθ)).